Quartz tuning forks (QTFs) are employed as sensitive elements for gas sensing applications implementing quartz-enhanced photoacoustic spectroscopy. Therefore, proper design of the QTF read-out electronics is required to optimize the signal-to-noise ratio (SNR), and in turn, the minimum detection limit of the gas concentration. In this work, we present a theoretical study of the SNR trend in a voltage-mode read-out of QTFs, mainly focusing on the effects of (i) the noise contributions of both the QTF-equivalent resistor and the input bias resistor R_L of the preamplifier, (ii) the operating frequency, and (iii) the bandwidth (BW) of the lock-in amplifier low-pass filter. A MATLAB model for the main noise contributions was retrieved and then validated by means of SPICE simulations. When the bandwidth of the lock-in filter is sufficiently narrow (BW = 0.5 Hz), the SNR values do not strongly depend on both the operating frequency and R_L values. On the other hand, when a wider low-pass filter bandwidth is employed (BW = 5 Hz), a sharp SNR peak close to the QTF parallel-resonant frequency is found for large values of R_L (R_L > 2 MΩ), whereas for small values of R_L (R_L < 2 MΩ), the SNR exhibits a peak around the QTF series-resonant frequency.

The quartz tuning fork used as an acoustic sensor in quartz-enhanced photo-acoustic spectroscopy gas detection systems is usually read out by means of a transimpedance preamplifier based on a low-noise operational amplifier closed in a feedback loop. The gain–bandwidth product of the operational amplifier used in the circuit is a key parameter which must be properly chosen to guarantee that the circuit works as expected. Here, we demonstrate that if the value of this parameter is not sufficiently large, the response of the preamplifier exhibits a peak at a frequency which does not coincide with the series resonant frequency of the quartz tuning fork. If this peak frequency is selected for modulating the laser bias current and is also used as the reference frequency of the lock-in amplifier, a penalty results in terms of signal-to-noise ratio at the output of the QEPAS sensor. This worsens the performance of the gas sensing system in terms of ultimate detection limits. We show that this happens when the front-end preamplifier of the quartz tuning fork is based on some amplifier models that are typically used for such application, both when the integration time of the lock-in amplifier filter is long, to boost noise rejection, and when it is short, in order to comply with a relevant measurement rate.

The quartz tuning fork used as an acoustic sensor in Quartz-Enhanced Photo-Acoustic Spectroscopy gas detection systems is usually read-out by means of a transimpedance preamplifier, based on a low-noise operational amplifier closed in a feedback loop. The gain-bandwidth product of the operational amplifier used in the circuit is a key parameter which must be properly chosen to guarantee that the circuit works as expected. Here we demonstrate that, if the value of this parameter is not sufficiently large, the response of the preamplifier exhibits a peak at a frequency which does not coincide with the series resonant frequency of the quartz tuning fork. If this peak frequency is selected for modulating the laser bias current and is also used as reference frequency of the lock-in amplifier, a penalty results in terms of signal to noise ratio at the output of the QEPAS sensor. This worsens the performance of the gas sensing system in terms of ultimate detection limits. We show that this happens when the front-end preamplifier of the quartz tuning fork is based on some amplifier models that are typically used for such application, both when the integration time of the lock-in amplifier filter is long, to boost noise rejection, and when it is short, in order to comply with a relevant measurement rate.